1 Read this first

This document is intended for audiences internal to the project team for the Boulder City, CO Guaranteed Income project (BGI). The data presented here is simulated or uses publicly available estimates for certain parameters (meaning there are no PII, IRB, or proprietary concerns with this document, but it should not be circulated beyond the core project team).

For team members interested in the process for weighting and selection the key sections are:

  • Section 2

  • Section 5

  • Section 5.2

For team members who are primarily interested in seeing an example of the spreadsheet that tracks each sampling wave, please see the Appendix in Section 6. The first table is the condensed version that shows just the IDs for each wave. The second table is the expanded version that shows the demographic characteristics for the individuals in each wave. The data can be downloaded via the clipboard or a csv file.

2 Summary

Steps in the weighting process:

  • 1st) Simulate population dataset based on questions from recruitment form. The simulated dataset is for illustrating the process. It represents an estimate of the total population of those living in 30 - 60% AMI in Boulder City.

  • 2nd) Randomly sample 4000 applicants from the simulated population data. Our interest is in evaluating what a weighted sample of this applicant pool looks like.

  • 3rd) Select first ‘wave’ of 200 program selections using two methods: A - a custom weighting procedure B - a purely random sample of 200 selections from the applicant pool

  • 4th) Select second and third waves using propensity score matching against the applicant pool ((Ho et al. 2011))1.

  • Last) Make the dataset with selections and backups available for download (see Section 6).

3 Requirements

  • Ideally, make all matches based on estimates of population in Boulder City who are either a) between 30 and 60 % of area median income (AMI) or b) below poverty line.

  • Proportionate match by race/ethnicty, gender identity, and disability status.

  • Individuals with children under 18 should be represented in the program at ~2xs their representation in the application pool.

4 Questionaire info

The eligibility questionnaire will have questions on each of the above, plus additional eligibility and other characteristics not addressed here.

Ethnicity/race options:

  • Hispanic/Latino

  • Black or African American

  • White (not Latino)

  • Asian

  • 2 or more races

  • Not listed

  • Native Hawaiian/Pacific Islander

  • American Indian/Alaskan Native

Gender:

  • Woman

  • Man

  • Transgender

  • Prefer to self identify (please write in your preferred identity here)

Households with children under 18

  • Yes

  • No

Disability status:

  • Yes
  • No

5 Estimates

This table shows the probabilities that we are working with in the current iteration of our fake data. These are based on empirical estimates.

Race and ethnicity: estimates derived from this City of Boulder online source. The poverty measure is the US census bureau’s definition of poverty.

Gender: estimates derived from the Williams Institute and are based on the entire state of CO. We only have estimates for percent transgender.

Children in household: estimates will be based on the applicant pool (the values in the table are placeholders).

Disability: studies have shown that about 25% of the population is disabled at any give time and we will use this as our background expectation for Boulder City.

Table 5.1: Parameters for weighting
sub_group target_props
race_ethnicity
White (not latino) 0.756
Hispanic 0.100
Black or African American 0.014
Asian 0.051
American Indian or Alaska Native 0.002
Native Hawaiian or Other Pacific Islander 0.001
Not Listed 0.021
Two or more 0.055
gender
Woman 0.440
Man 0.440
Transgender 0.060
Prefer to self identify 0.060
child_household
No 0.800
Yes 0.200
disability
No 0.750
Yes 0.250

5.1 Simulated data

5.1.1 Population

Start with data represents a loosely informed estimate of the ‘total population’.

A few example rows from the simulated population sample:

Table 5.2: Sample rows from our fake data
id race_ethnicity gender child_household disability
19526 White (not latino) Man No Yes
2295 White (not latino) Woman No No
6964 White (not latino) Man No No
7717 White (not latino) Prefer to self identify Yes Yes
519 White (not latino) Man Yes No
24333 White (not latino) Man No No
16499 White (not latino) Woman No No
607 White (not latino) Man Yes No
18385 Asian Man No No
11269 White (not latino) Man No Yes

5.1.2 Enrollees

Randomly select 4000 from the population.

Table 5.3: Proportions in randomly selected enrollee data
sub_group count proportions target_proportions
child_household
No 3274 0.819 0.800
Yes 726 0.182 0.200
disability
No 2979 0.745 0.750
Yes 1021 0.255 0.250
gender
Man 1727 0.432 0.440
Prefer to self identify 259 0.065 0.060
Transgender 242 0.060 0.060
Woman 1772 0.443 0.440
race_ethnicity
American Indian or Alaska Native 6 0.002 0.002
Asian 185 0.046 0.051
Black or African American 58 0.015 0.014
Hispanic 415 0.104 0.100
Native Hawaiian or Other Pacific Islander 7 0.002 0.001
Not Listed 82 0.020 0.021
Two or more 231 0.058 0.055
White (not latino) 3016 0.754 0.756

Note: as a reminder/clarifier, in the above table the ‘proportions’ column is what we observe when we select 4000 rows/individuals from our simulated population data. The target_proportions are the values used to simulate the population data.

5.1.3 Select sample 1

To select the first sample wave of 200 individuals from our 4000 applicant pool we first take a custom weighted sample of the data using the target proportions in Table 5.3.

The customized weighting procedure:

  • calculate the expected number of individuals in a sample of 200 if they were in the sample at exactly their expected proportions.

    • For any cases where the expected number of people is less than one person, round up to one person. This seems like a small effect but consider that for a rare characteristic we might expect 0.2 people to have that characteristics in a sample of
      1. By rounding up to one we have increased the odds that someone with this characteristic gets selected by 5xs.
    • Calculate the number of people in the applicant pool who have children under the age of 18 and double the expected number.

  • For any individuals that have expected counts <= 3, add three to their expected count. This is another way of increasing proportionate representation of rare characteristics.

  • Reserve 25% of the target sample size of 200 and for individuals with rare characteristics. These are defined by examining the applicant pool and simply counting the characteristics of all the people in the pool. A random sample of 50 (25% of 200) of the rarest 50% of characteristics are reserved for the final selected sample.

  • The remaining 75% are chosen by a simple weighting from the enrollee pool.

  • Lastly, if any characteristics are present in the enrollee pool but still missing the selected sample, select one person at random with that characteristic and replace someone chosen at random with the most common set of characteritics.

The target proportions in Table 5.3 are based on characteristics of participants, so this first step in the sampling selects more than 200. We then select 200 people for the first sampling wave using the procedure just described.

Table 5.4: Comparing a random sample to custom weighted sample
sub_group props target_counts count_rand proportions_rand count_w proportions_w
race_ethnicity
American Indian or Alaska Native 0.002 1 NA NA 3 0.014925373
Native Hawaiian or Other Pacific Islander 0.001 1 NA NA 1 0.004975124
Black or African American 0.014 3 2 0.010 5 0.024875622
Not Listed 0.021 4 2 0.010 8 0.039800995
Asian 0.051 10 13 0.065 18 0.089552239
Two or more 0.055 11 11 0.055 21 0.104477612
Hispanic 0.100 20 23 0.115 18 0.089552239
White (not latino) 0.756 151 149 0.745 127 0.631840796
gender
Transgender 0.060 12 14 0.070 17 0.084577114
Prefer to self identify 0.060 12 11 0.055 26 0.129353234
Man 0.440 88 84 0.420 53 0.263681592
Woman 0.440 88 91 0.455 105 0.522388060
child_household
Yes 0.200 40 40 0.200 48 0.238805970
No 0.800 160 160 0.800 153 0.761194030
disability
Yes 0.250 50 47 0.235 48 0.238805970
No 0.750 150 153 0.765 153 0.761194030

NOTE: A visual inspection of the above table will often suggest that low sample size groups are being dropped from the random (non-weighted) selection procedure. The inadvertent dropping of some rare characteristics can happen and this highlights an advantage of the customized weighted selection procedure. However, another approach could be to take lots of random samples (like, 30) and then average across them. This would at least prevent rare groups from being complete dropped.

Discussion points could center on how ‘individuals with rare characteristics’ are defined. Currently these are simply the lower half of the characteristics ranked by frequency, but other definitions are certainly possible. Another discussion point could be the fraction of the final sample reserved for individuals with rare characteristics. 25% is a reasonable starting point but this could be increased or decreased.

5.1.4 Select samples 2 and 3

The second wave selection works by taking the wave 1 selection and then using an algorithm to find each individual’s closest match from the 3800 individuals remaining in the applicant pool. This is done using a technique called propensity score matching (Ho et al. 2011).

The third wave of sampled individuals is done with the same process.

5.2 Visualize the sampling waves

5.2.1 Applicant data and population estimates

First, compare the population data to the applicant data:

Proportions by race group in simulated population data.

Figure 5.1: Proportions by race group in simulated population data.

Proportions by gender in simulated population data.

Figure 5.2: Proportions by gender in simulated population data.

We can examine just the race and gender breakdowns, above, to see that randomly sampling 4000 individuals from our population of 25000 leads to proportions in each group that are fairly similar.

5.2.2 Proportions in each sampling wave

Next, we can see how the proportions in each sampling wave compare to the ‘target’ proportions in the population data.

First with a table showing counts and proportions for each sampling wave compared to the population.

Table 5.5: Results across three sampling waves
sub_group target_props target_counts count_w1 props_w1 count_w2 props_w2 count_w3 props_w3
race_ethnicity
American Indian or Alaska Native 0.002 1 3 0.015 3 0.015 NA NA
Native Hawaiian or Other Pacific Islander 0.001 1 1 0.005 NA NA NA NA
Black or African American 0.014 3 5 0.025 6 0.030 7 0.035
Not Listed 0.021 4 8 0.040 9 0.045 10 0.050
Asian 0.051 10 18 0.090 19 0.095 19 0.095
Two or more 0.055 11 21 0.104 20 0.100 21 0.104
Hispanic 0.100 20 18 0.090 17 0.085 17 0.085
White (not latino) 0.756 151 127 0.632 127 0.632 127 0.632
gender
Transgender 0.060 12 17 0.085 17 0.085 16 0.080
Prefer to self identify 0.060 12 26 0.129 26 0.129 29 0.144
Man 0.440 88 53 0.264 54 0.269 54 0.269
Woman 0.440 88 105 0.522 104 0.517 102 0.507
child_household
Yes 0.200 40 48 0.239 48 0.239 48 0.239
No 0.800 160 153 0.761 153 0.761 153 0.761
disability
Yes 0.250 50 48 0.239 47 0.234 47 0.234
No 0.750 150 153 0.761 154 0.766 154 0.766

5.2.2.1 Race by sampling wave

Proportions by racial grouping, sampling waves.

Figure 5.3: Proportions by racial grouping, sampling waves.

5.2.2.2 Gender by sampling wave

Proportions by gender, sampling waves.

Figure 5.4: Proportions by gender, sampling waves.

5.2.2.3 Child in household by sampling wave

Proportions of households with a child in the home, by sampling wave.

Figure 5.5: Proportions of households with a child in the home, by sampling wave.

5.2.2.4 Disability status by sampling wave

Proportions by disability status, sampling wave.

Figure 5.6: Proportions by disability status, sampling wave.

6 Appendix A: Example datasets

The first example dataset presents a column for each sampling wave. The intended use is that all the individuals in the far left column, Wave 1, are selected to the program for verification. If some of these individuals cannot be verified, their replacement is the cell in the same row immediately to the right, in the Wave 2 column. If someone in Wave 2 cannot be verified, then proceed to Wave 3.

These are for illustration and to aid in thinking through the tracking process. A strategy, yet to be defined, will be used for selecting cases beyond the first three sampling waves.

Table 6.1: Suggested format for the ‘simple’ version of the sample waves using the example data generated above.
Table 6.2: Suggested format for the extended, wide, version of the sample waves using the example data generated above showing all attributes for each matched sample wave.

References

Ho, Daniel E., Kosuke Imai, Gary King, and Elizabeth A. Stuart. 2011. “MatchIt: Nonparametric Preprocessing for Parametric Causal Inference” 42. https://doi.org/10.18637/jss.v042.i08.

  1. Propensity score matching is a technique often used in quasi-experimental designs for statistically matching members of a treatment group to members of a control group. In our case, we use the same kind of algorithm to match each participant in sampling waves 2 and 3 with their most similar counter part in the applicant pool.↩︎